Topics on multirate systems: frequency response, interpolation, model validation

We address several topics on multirate systems, mostly in a frequency domain point of view. We first study the frequency response of a multirate system and derive the aliasing component (AC) representation. We give the relationship between the AC representation and the usual transfer function matrix of the lifted LTI system. Next, we propose a multirate version of the Nevanlina-Pick (NP) interpolation problem and give a necessary and sufficient solvability condition. This version of the NP interpolation problem is of interest mathematically and has potential applications in addressing other issues in control, signal processing and circuit theory. Finally, as an application of the multirate version of the NP interpolation problem, we formulate and solve the robust model validation problem for multirate systems with frequency domain experiment data.